{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy\n",
    "from sympy import MatrixSymbol\n",
    "from sympy.matrices.expressions import Trace\n",
    "sympy.init_printing()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The least squares for classification model is defined as a linear model of the form\n",
    "\n",
    "$$\n",
    "    y_k({\\bf x}) = {\\bf w}_k^T{\\bf x} + w_{k0}\n",
    "$$\n",
    "\n",
    "To group all these elements, we consider the matrices $T \\in \\mathcal{M}_{N, K}(\\{0, 1\\})$ and $\\tilde{\\bf X} \\in \\mathcal{M}_{N, D + 1}(\\mathbb{R})$. The error function is then defined as\n",
    "    \n",
    "$$\n",
    "    E_D(\\tilde{\\bf W}) = \\frac{1}{2}\\text{Tr}\\left\\{\\left(\\tilde{\\bf X}\\tilde{\\bf W} - T\\right)^T\\left(\\tilde{\\bf X}\\tilde{\\bf W} - T\\right)\\right\\} \n",
    "$$\n",
    "\n",
    "Where $\\tilde{\\bf W} \\in \\mathcal{M}_{D+1, K}(\\mathbb{R})$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "D, N, K = 3, 5, 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left( \\tilde X, \\  \\tilde W, \\  T\\right)$"
      ],
      "text/plain": [
       "(\\tilde X, \\tilde W, T)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = MatrixSymbol(r\"\\tilde X\", N, D + 1)\n",
    "W = MatrixSymbol(r\"\\tilde W\", D + 1, K)\n",
    "T = MatrixSymbol(\"T\", N, K)\n",
    "\n",
    "X, W, T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "Err = (X @ W - T).T @ (X @ W - T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\left(- T_{0, 0} + \\tilde W_{0, 0} \\tilde X_{0, 0} + \\tilde W_{1, 0} \\tilde X_{0, 1} + \\tilde W_{2, 0} \\tilde X_{0, 2} + \\tilde W_{3, 0} \\tilde X_{0, 3}\\right)^{2} + \\left(- T_{1, 0} + \\tilde W_{0, 0} \\tilde X_{1, 0} + \\tilde W_{1, 0} \\tilde X_{1, 1} + \\tilde W_{2, 0} \\tilde X_{1, 2} + \\tilde W_{3, 0} \\tilde X_{1, 3}\\right)^{2} + \\left(- T_{2, 0} + \\tilde W_{0, 0} \\tilde X_{2, 0} + \\tilde W_{1, 0} \\tilde X_{2, 1} + \\tilde W_{2, 0} \\tilde X_{2, 2} + \\tilde W_{3, 0} \\tilde X_{2, 3}\\right)^{2} + \\left(- T_{3, 0} + \\tilde W_{0, 0} \\tilde X_{3, 0} + \\tilde W_{1, 0} \\tilde X_{3, 1} + \\tilde W_{2, 0} \\tilde X_{3, 2} + \\tilde W_{3, 0} \\tilde X_{3, 3}\\right)^{2} + \\left(- T_{4, 0} + \\tilde W_{0, 0} \\tilde X_{4, 0} + \\tilde W_{1, 0} \\tilde X_{4, 1} + \\tilde W_{2, 0} \\tilde X_{4, 2} + \\tilde W_{3, 0} \\tilde X_{4, 3}\\right)^{2} & \\left(- T_{0, 0} + \\tilde W_{0, 0} \\tilde X_{0, 0} + \\tilde W_{1, 0} \\tilde X_{0, 1} + \\tilde W_{2, 0} \\tilde X_{0, 2} + \\tilde W_{3, 0} \\tilde X_{0, 3}\\right) \\left(- T_{0, 1} + \\tilde W_{0, 1} \\tilde X_{0, 0} + \\tilde W_{1, 1} \\tilde X_{0, 1} + \\tilde W_{2, 1} \\tilde X_{0, 2} + \\tilde W_{3, 1} \\tilde X_{0, 3}\\right) + \\left(- T_{1, 0} + \\tilde W_{0, 0} \\tilde X_{1, 0} + \\tilde W_{1, 0} \\tilde X_{1, 1} + \\tilde W_{2, 0} \\tilde X_{1, 2} + \\tilde W_{3, 0} \\tilde X_{1, 3}\\right) \\left(- T_{1, 1} + \\tilde W_{0, 1} \\tilde X_{1, 0} + \\tilde W_{1, 1} \\tilde X_{1, 1} + \\tilde W_{2, 1} \\tilde X_{1, 2} + \\tilde W_{3, 1} \\tilde X_{1, 3}\\right) + \\left(- T_{2, 0} + \\tilde W_{0, 0} \\tilde X_{2, 0} + \\tilde W_{1, 0} \\tilde X_{2, 1} + \\tilde W_{2, 0} \\tilde X_{2, 2} + \\tilde W_{3, 0} \\tilde X_{2, 3}\\right) \\left(- T_{2, 1} + \\tilde W_{0, 1} \\tilde X_{2, 0} + \\tilde W_{1, 1} \\tilde X_{2, 1} + \\tilde W_{2, 1} \\tilde X_{2, 2} + \\tilde W_{3, 1} \\tilde X_{2, 3}\\right) + \\left(- T_{3, 0} + \\tilde W_{0, 0} \\tilde X_{3, 0} + \\tilde W_{1, 0} \\tilde X_{3, 1} + \\tilde W_{2, 0} \\tilde X_{3, 2} + \\tilde W_{3, 0} \\tilde X_{3, 3}\\right) \\left(- T_{3, 1} + \\tilde W_{0, 1} \\tilde X_{3, 0} + \\tilde W_{1, 1} \\tilde X_{3, 1} + \\tilde W_{2, 1} \\tilde X_{3, 2} + \\tilde W_{3, 1} \\tilde X_{3, 3}\\right) + \\left(- T_{4, 0} + \\tilde W_{0, 0} \\tilde X_{4, 0} + \\tilde W_{1, 0} \\tilde X_{4, 1} + \\tilde W_{2, 0} \\tilde X_{4, 2} + \\tilde W_{3, 0} \\tilde X_{4, 3}\\right) \\left(- T_{4, 1} + \\tilde W_{0, 1} \\tilde X_{4, 0} + \\tilde W_{1, 1} \\tilde X_{4, 1} + \\tilde W_{2, 1} \\tilde X_{4, 2} + \\tilde W_{3, 1} \\tilde X_{4, 3}\\right)\\\\\\left(- T_{0, 0} + \\tilde W_{0, 0} \\tilde X_{0, 0} + \\tilde W_{1, 0} \\tilde X_{0, 1} + \\tilde W_{2, 0} \\tilde X_{0, 2} + \\tilde W_{3, 0} \\tilde X_{0, 3}\\right) \\left(- T_{0, 1} + \\tilde W_{0, 1} \\tilde X_{0, 0} + \\tilde W_{1, 1} \\tilde X_{0, 1} + \\tilde W_{2, 1} \\tilde X_{0, 2} + \\tilde W_{3, 1} \\tilde X_{0, 3}\\right) + \\left(- T_{1, 0} + \\tilde W_{0, 0} \\tilde X_{1, 0} + \\tilde W_{1, 0} \\tilde X_{1, 1} + \\tilde W_{2, 0} \\tilde X_{1, 2} + \\tilde W_{3, 0} \\tilde X_{1, 3}\\right) \\left(- T_{1, 1} + \\tilde W_{0, 1} \\tilde X_{1, 0} + \\tilde W_{1, 1} \\tilde X_{1, 1} + \\tilde W_{2, 1} \\tilde X_{1, 2} + \\tilde W_{3, 1} \\tilde X_{1, 3}\\right) + \\left(- T_{2, 0} + \\tilde W_{0, 0} \\tilde X_{2, 0} + \\tilde W_{1, 0} \\tilde X_{2, 1} + \\tilde W_{2, 0} \\tilde X_{2, 2} + \\tilde W_{3, 0} \\tilde X_{2, 3}\\right) \\left(- T_{2, 1} + \\tilde W_{0, 1} \\tilde X_{2, 0} + \\tilde W_{1, 1} \\tilde X_{2, 1} + \\tilde W_{2, 1} \\tilde X_{2, 2} + \\tilde W_{3, 1} \\tilde X_{2, 3}\\right) + \\left(- T_{3, 0} + \\tilde W_{0, 0} \\tilde X_{3, 0} + \\tilde W_{1, 0} \\tilde X_{3, 1} + \\tilde W_{2, 0} \\tilde X_{3, 2} + \\tilde W_{3, 0} \\tilde X_{3, 3}\\right) \\left(- T_{3, 1} + \\tilde W_{0, 1} \\tilde X_{3, 0} + \\tilde W_{1, 1} \\tilde X_{3, 1} + \\tilde W_{2, 1} \\tilde X_{3, 2} + \\tilde W_{3, 1} \\tilde X_{3, 3}\\right) + \\left(- T_{4, 0} + \\tilde W_{0, 0} \\tilde X_{4, 0} + \\tilde W_{1, 0} \\tilde X_{4, 1} + \\tilde W_{2, 0} \\tilde X_{4, 2} + \\tilde W_{3, 0} \\tilde X_{4, 3}\\right) \\left(- T_{4, 1} + \\tilde W_{0, 1} \\tilde X_{4, 0} + \\tilde W_{1, 1} \\tilde X_{4, 1} + \\tilde W_{2, 1} \\tilde X_{4, 2} + \\tilde W_{3, 1} \\tilde X_{4, 3}\\right) & \\left(- T_{0, 1} + \\tilde W_{0, 1} \\tilde X_{0, 0} + \\tilde W_{1, 1} \\tilde X_{0, 1} + \\tilde W_{2, 1} \\tilde X_{0, 2} + \\tilde W_{3, 1} \\tilde X_{0, 3}\\right)^{2} + \\left(- T_{1, 1} + \\tilde W_{0, 1} \\tilde X_{1, 0} + \\tilde W_{1, 1} \\tilde X_{1, 1} + \\tilde W_{2, 1} \\tilde X_{1, 2} + \\tilde W_{3, 1} \\tilde X_{1, 3}\\right)^{2} + \\left(- T_{2, 1} + \\tilde W_{0, 1} \\tilde X_{2, 0} + \\tilde W_{1, 1} \\tilde X_{2, 1} + \\tilde W_{2, 1} \\tilde X_{2, 2} + \\tilde W_{3, 1} \\tilde X_{2, 3}\\right)^{2} + \\left(- T_{3, 1} + \\tilde W_{0, 1} \\tilde X_{3, 0} + \\tilde W_{1, 1} \\tilde X_{3, 1} + \\tilde W_{2, 1} \\tilde X_{3, 2} + \\tilde W_{3, 1} \\tilde X_{3, 3}\\right)^{2} + \\left(- T_{4, 1} + \\tilde W_{0, 1} \\tilde X_{4, 0} + \\tilde W_{1, 1} \\tilde X_{4, 1} + \\tilde W_{2, 1} \\tilde X_{4, 2} + \\tilde W_{3, 1} \\tilde X_{4, 3}\\right)^{2}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎣(-T₀₀ + \\tilde W₀₀⋅\\tilde X₀₀ + \\tilde W₁₀⋅\\tilde X₀₁ + \\tilde W₂₀⋅\\tilde X₀₂\n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       " + \\tilde W₃₀⋅\\tilde X₀₃)⋅(-T₀₁ + \\tilde W₀₁⋅\\tilde X₀₀ + \\tilde W₁₁⋅\\tilde X₀\n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "₁ + \\tilde W₂₁⋅\\tilde X₀₂ + \\tilde W₃₁⋅\\tilde X₀₃) + (-T₁₀ + \\tilde W₀₀⋅\\tilde\n",
       "\n",
       "                                                                              \n",
       "                      (-T₀₀ + \\tilde W₀₀⋅\\tilde X₀₀ + \\tilde W₁₀⋅\\tilde X₀₁ + \n",
       "                                                                              \n",
       "                                                                              \n",
       " X₁₀ + \\tilde W₁₀⋅\\tilde X₁₁ + \\tilde W₂₀⋅\\tilde X₁₂ + \\tilde W₃₀⋅\\tilde X₁₃)⋅\n",
       "\n",
       "                                              2                               \n",
       "\\tilde W₂₀⋅\\tilde X₀₂ + \\tilde W₃₀⋅\\tilde X₀₃)  + (-T₁₀ + \\tilde W₀₀⋅\\tilde X₁\n",
       "                                                                              \n",
       "                                                                              \n",
       "(-T₁₁ + \\tilde W₀₁⋅\\tilde X₁₀ + \\tilde W₁₁⋅\\tilde X₁₁ + \\tilde W₂₁⋅\\tilde X₁₂ \n",
       "\n",
       "                                                                          2   \n",
       "₀ + \\tilde W₁₀⋅\\tilde X₁₁ + \\tilde W₂₀⋅\\tilde X₁₂ + \\tilde W₃₀⋅\\tilde X₁₃)  + \n",
       "                                                                              \n",
       "                                                                              \n",
       "+ \\tilde W₃₁⋅\\tilde X₁₃) + (-T₂₀ + \\tilde W₀₀⋅\\tilde X₂₀ + \\tilde W₁₀⋅\\tilde X\n",
       "\n",
       "                                                                              \n",
       "(-T₂₀ + \\tilde W₀₀⋅\\tilde X₂₀ + \\tilde W₁₀⋅\\tilde X₂₁ + \\tilde W₂₀⋅\\tilde X₂₂ \n",
       "                                                                              \n",
       "                                                                              \n",
       "₂₁ + \\tilde W₂₀⋅\\tilde X₂₂ + \\tilde W₃₀⋅\\tilde X₂₃)⋅(-T₂₁ + \\tilde W₀₁⋅\\tilde \n",
       "\n",
       "                        2                                                     \n",
       "+ \\tilde W₃₀⋅\\tilde X₂₃)  + (-T₃₀ + \\tilde W₀₀⋅\\tilde X₃₀ + \\tilde W₁₀⋅\\tilde \n",
       "                                                                              \n",
       "                                                                              \n",
       "X₂₀ + \\tilde W₁₁⋅\\tilde X₂₁ + \\tilde W₂₁⋅\\tilde X₂₂ + \\tilde W₃₁⋅\\tilde X₂₃) +\n",
       "\n",
       "                                                    2                         \n",
       "X₃₁ + \\tilde W₂₀⋅\\tilde X₃₂ + \\tilde W₃₀⋅\\tilde X₃₃)  + (-T₄₀ + \\tilde W₀₀⋅\\ti\n",
       "                                                                              \n",
       "                                                                              \n",
       " (-T₃₀ + \\tilde W₀₀⋅\\tilde X₃₀ + \\tilde W₁₀⋅\\tilde X₃₁ + \\tilde W₂₀⋅\\tilde X₃₂\n",
       "\n",
       "                                                                              \n",
       "lde X₄₀ + \\tilde W₁₀⋅\\tilde X₄₁ + \\tilde W₂₀⋅\\tilde X₄₂ + \\tilde W₃₀⋅\\tilde X₄\n",
       "                                                                              \n",
       "                                                                              \n",
       " + \\tilde W₃₀⋅\\tilde X₃₃)⋅(-T₃₁ + \\tilde W₀₁⋅\\tilde X₃₀ + \\tilde W₁₁⋅\\tilde X₃\n",
       "\n",
       "  2                                                                           \n",
       "₃)                                                                            \n",
       "                                                                              \n",
       "                                                                              \n",
       "₁ + \\tilde W₂₁⋅\\tilde X₃₂ + \\tilde W₃₁⋅\\tilde X₃₃) + (-T₄₀ + \\tilde W₀₀⋅\\tilde\n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       " X₄₀ + \\tilde W₁₀⋅\\tilde X₄₁ + \\tilde W₂₀⋅\\tilde X₄₂ + \\tilde W₃₀⋅\\tilde X₄₃)⋅\n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "(-T₄₁ + \\tilde W₀₁⋅\\tilde X₄₀ + \\tilde W₁₁⋅\\tilde X₄₁ + \\tilde W₂₁⋅\\tilde X₄₂ \n",
       "\n",
       "                                                                              \n",
       "                          (-T₀₀ + \\tilde W₀₀⋅\\tilde X₀₀ + \\tilde W₁₀⋅\\tilde X₀\n",
       "                                                                              \n",
       "                                                                              \n",
       "+ \\tilde W₃₁⋅\\tilde X₄₃)                                                      \n",
       "\n",
       "                                                                              \n",
       "₁ + \\tilde W₂₀⋅\\tilde X₀₂ + \\tilde W₃₀⋅\\tilde X₀₃)⋅(-T₀₁ + \\tilde W₀₁⋅\\tilde X\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "₀₀ + \\tilde W₁₁⋅\\tilde X₀₁ + \\tilde W₂₁⋅\\tilde X₀₂ + \\tilde W₃₁⋅\\tilde X₀₃) + \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "(-T₁₀ + \\tilde W₀₀⋅\\tilde X₁₀ + \\tilde W₁₀⋅\\tilde X₁₁ + \\tilde W₂₀⋅\\tilde X₁₂ \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                               (-T₀₁ + \\tilde W₀₁⋅\\tilde X₀₀ +\n",
       "\n",
       "                                                                              \n",
       "+ \\tilde W₃₀⋅\\tilde X₁₃)⋅(-T₁₁ + \\tilde W₀₁⋅\\tilde X₁₀ + \\tilde W₁₁⋅\\tilde X₁₁\n",
       "                                                                              \n",
       "                                                                       2      \n",
       " \\tilde W₁₁⋅\\tilde X₀₁ + \\tilde W₂₁⋅\\tilde X₀₂ + \\tilde W₃₁⋅\\tilde X₀₃)  + (-T\n",
       "\n",
       "                                                                              \n",
       " + \\tilde W₂₁⋅\\tilde X₁₂ + \\tilde W₃₁⋅\\tilde X₁₃) + (-T₂₀ + \\tilde W₀₀⋅\\tilde \n",
       "                                                                              \n",
       "                                                                              \n",
       "₁₁ + \\tilde W₀₁⋅\\tilde X₁₀ + \\tilde W₁₁⋅\\tilde X₁₁ + \\tilde W₂₁⋅\\tilde X₁₂ + \\\n",
       "\n",
       "                                                                              \n",
       "X₂₀ + \\tilde W₁₀⋅\\tilde X₂₁ + \\tilde W₂₀⋅\\tilde X₂₂ + \\tilde W₃₀⋅\\tilde X₂₃)⋅(\n",
       "                                                                              \n",
       "                     2                                                        \n",
       "tilde W₃₁⋅\\tilde X₁₃)  + (-T₂₁ + \\tilde W₀₁⋅\\tilde X₂₀ + \\tilde W₁₁⋅\\tilde X₂₁\n",
       "\n",
       "                                                                              \n",
       "-T₂₁ + \\tilde W₀₁⋅\\tilde X₂₀ + \\tilde W₁₁⋅\\tilde X₂₁ + \\tilde W₂₁⋅\\tilde X₂₂ +\n",
       "                                                                              \n",
       "                                                 2                            \n",
       " + \\tilde W₂₁⋅\\tilde X₂₂ + \\tilde W₃₁⋅\\tilde X₂₃)  + (-T₃₁ + \\tilde W₀₁⋅\\tilde\n",
       "\n",
       "                                                                              \n",
       " \\tilde W₃₁⋅\\tilde X₂₃) + (-T₃₀ + \\tilde W₀₀⋅\\tilde X₃₀ + \\tilde W₁₀⋅\\tilde X₃\n",
       "                                                                              \n",
       "                                                                             2\n",
       " X₃₀ + \\tilde W₁₁⋅\\tilde X₃₁ + \\tilde W₂₁⋅\\tilde X₃₂ + \\tilde W₃₁⋅\\tilde X₃₃) \n",
       "\n",
       "                                                                              \n",
       "₁ + \\tilde W₂₀⋅\\tilde X₃₂ + \\tilde W₃₀⋅\\tilde X₃₃)⋅(-T₃₁ + \\tilde W₀₁⋅\\tilde X\n",
       "                                                                              \n",
       "                                                                              \n",
       " + (-T₄₁ + \\tilde W₀₁⋅\\tilde X₄₀ + \\tilde W₁₁⋅\\tilde X₄₁ + \\tilde W₂₁⋅\\tilde X\n",
       "\n",
       "                                                                              \n",
       "₃₀ + \\tilde W₁₁⋅\\tilde X₃₁ + \\tilde W₂₁⋅\\tilde X₃₂ + \\tilde W₃₁⋅\\tilde X₃₃) + \n",
       "                                                                              \n",
       "                           2                                                  \n",
       "₄₂ + \\tilde W₃₁⋅\\tilde X₄₃)                                                   \n",
       "\n",
       "                                                                              \n",
       "(-T₄₀ + \\tilde W₀₀⋅\\tilde X₄₀ + \\tilde W₁₀⋅\\tilde X₄₁ + \\tilde W₂₀⋅\\tilde X₄₂ \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "+ \\tilde W₃₀⋅\\tilde X₄₃)⋅(-T₄₁ + \\tilde W₀₁⋅\\tilde X₄₀ + \\tilde W₁₁⋅\\tilde X₄₁\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                 ⎤\n",
       " + \\tilde W₂₁⋅\\tilde X₄₂ + \\tilde W₃₁⋅\\tilde X₄₃)⎥\n",
       "                                                 ⎥\n",
       "                                                 ⎥\n",
       "                                                 ⎦"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Err.as_explicit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAUkAAAAmCAYAAABJX2mTAAAACXBIWXMAAA7EAAAOxAGVKw4bAAALuklEQVR4Ae2di5XdNBCG2ZwUsIQKCB0EqCChgxAqgHQQTirgQAchFUDSQaCCkO0goQIgHYT/82oc29cPjS3p+u6VztHalsajefwa62Hfvfjw4cMnx0gXFxc/0K7a/zWmfS99DM9Kc3MtILxcSrvnwte3ubSsmMxl2fV8vX6Pob+9Xpz1d0qwJ7r7OwH4yxguXvoYnpXmZltA2Hov3DxTfhOLM49FKiY91ipH6/V7DP2FiMppoJYErgc6vFD+HAGXGvfSL/Gr9edlgRDMvhbWko0oKyb3jyGv3+foiwZJCcIU6G/l+wLt1ZKpvfRL/Gr9eVpAOHojzZ8Jc1FLO3NWqpics86+6rx+n6IvHSQZQbIOGfVUl9Au+lIuklysp/6s/Ifyv8p3lRkhvwzXd3R8qPw4RccUn6OnY+q8tW3dj3/eKn8qfyzOXuaMLV67xOSczOda5/X7JL1AQ9DKnuWoe8rM7e/GtOelj+GZikay0VEujZ/OCZq6/GjHUPagW3bMc8mD/RlRvQqyMaonkEfJKLqkOotftDwp2g48XmzxQZA5GsNb2jq1ez3+XNItMS9wG+13aIf0t1RQKj1XQy9loHeRDXrpI9luI9PThuDyWnp0RyRsQDGq7CZGmLG6du9Lfh5kZqR7X/lH5W+UCZg8sIZyq7ifUuvskSdh2z9Jq4eBX1/B+KtdYjJe/DyUHn8uSZCSV2jL6/dD+qWonqJewjLdiX4Ce+lTyBjLQ7IxAmpHkdynxFTu5y4PXUeN0Lr37PVcuhxN55RtixcPhidr7Kz7XBhe00a95+NMLKUtvH4f0hdZk9TT4ZkaJmh8oeNi8tIvMsxIEJ58/6mJb6Tf4qgsoyjFWB9T5y1t695mLVl++tRrLN3rwrCXf6XPZwGv34f0pabbj2QCQBabvPSxfHPQfRWY/pWD+U55HlPnLW3zELtUJ2DpwZtOCZNe3W46vdfvPfrsQVKAZJrCOl7UKMtLv8a7tKH8Qfk/5VfKL0KmjNwtexPK2M0eS6zvvdPopLtGOUaXvUxyPlF+G+Q1PdqAoHL0RGfqoOMa3zRJ56zZ2f0cm6+irL5zdOsML2XsajaGPx8VNEnnBC+ztcnOxtIwuds2BvIRa8T4CR7RSXK5MBzNeEBIO8rongKXA+5pLyXjJn/q/lJYZUfV5fcDehW0O9syY/J1NPE82Pnttjk899IP74+5VhsEvN4aIvcpMW1+O+ShMkbBPwzLwz3sFkfvno3xSFkmWQiKKHOgX5AX3akf9bXKWX+c1Uf1q3WGtzLtH9iTslDfW/Pt2kf1q9sO+tM+X+G0uF86D3KJLP6eNbRqJxku17S/5h7JvNqfujc7Vk2nIGe037v07UhSkZ0RRdT7i6LzJHZ+Pbu8XnqPLEbLri67vG2S/nOjBRb8p3TA0XTcJElyMJprR1grmJqc7QjRyYPPRZdwsEVndg9Jj68P13+lM8GZdd1vlRntTaUtbcPztTJteVIJTCJPSlxO6pcAY13eW/xZAqsmq9fvLX0bJMWJNZccCVCbMWL4e+ljeLY0oTOOBTXaJY3VEXAO1hwDL+45qKPwSIlXj0h3rg8f/0pe9LApLA+FXlL9YgDaqrMCIF9ake8ZLx2R5elScDZ60W6xd4PF0KZYRaWsmESCoNsY9ty4jNIoEdEWf0qErFgdqOj1e0vfBEk5iI7j2VgZtD97SQfwBEkv/WzjY5Vy7NjnabZONbZ2eqV72tGN7PVAmWkGmfRU11NrltcUhf525MSOw9Ts7oZCAuYwTe7QJ9bZRh/YDTlZGpgcvSZu27DoGU1mxySO2IrLoTMLXrv8aXLlwqrxHxy9fm/pbwuAdBwLENb54f+blHgJQHVOAAAoGIObv1amnKmRMdPlZOI9Qk/y0kfzlryMYsZSM1roOK6lUVkvcIbrXllLvI8TAnovCIZghK/MX591RVU9U/zJB2VKncULXCEjD2fknAyQqiN4YOtU9jb9D0batDWTsmGSNqXjZlzOyJ61yuvPgTDJsTrgb5dev7f0t6Tgr8qAlMI/OA/5Jdx1ThlrMiR7z5FgyZPYpgLUHSR1BOuoGGIxeekXGUYSqF0eAMiaqiNGtpyNjGnMMAjwHTk+NV+Yb5jqNeeqN2BkE6zD2Ebzr9SuydSpznPaaavVf64ls41oislo8pwYLtf6swhWvX7v0t8yh0Qc6UDsiPJp4XtlXkQ3w0zdPuyoU3RW7qW3+7YeLdiPrQlt5X2M++nQbRBQZ2PE9lsQBFCSeDBYYj3wF7sodLT2nxZqb9hMbyQ9rOxcHwuTiHBKuFzrz9JYjfW7QeCz23YWeZyaEkzdbh3VOuYUnZVH0Yen+5+6yejt/qkjjvhegWBKfltuKDaSlA4sYVgn6MqNTndU/123MJzzPubs1DTQNfbGTqJHd3ZNbWbAj9FC1nR+nSND0YeD2mRab28XsJv/0ORDsEIpFjtGt4hh6QHtbnApeXJirHXTRn+Wxqr5s5V/4eTSGyQXgTLRoPdpPEsfOr4tAUw06SomUBR9IVw6WJDoCUrAUAFBbcvIzqbNBFvWnIcj/vcqM7CwWTMqS0+wRBehQ/Hbju90zrIN+j5WboJ4omZysJnFJA1KJ+y6G1xO+TURxhobJ/DnbrHaKKg/k9NtKb/lXT3jD2g8yUvv4T1KKz2ZJhAwio0iRwVJW2h2nAr+POwsgE5u1qQVqXnNhZENL6pfwTscm2Wc4IfUTR7wUzv4mmQ2ur6a/htLN81hRc0p4FIypvCn2TcrVr1+79J3gyTCdp+WtkmzwsXtLTbyvGxL5k+89PPc4mpxDqnolPO6yWx//wmc2YQbG6Hha3zCdNye5NmEgbFAx0OXTZrhw4iORio1mjWMx+5WHwOT2GPXuEzoz1JY9fq9pe8Gyb/kmHt4ZyLFBrr2dnUIOiMparHUS3/NevNfW+Mbdt7NjI/IwOzONHYs0fFZXtgypR/jO1qmDsX7pF+MBEhGk7YUwLfAboyNNjhfaG1Y8JulPhImkWm3uEzsz1JYdfld9m/p2yApMNChrjCAMk/35gmvc96dZJTFtNQ+amcdKTZhBO6NTV76WL4tHfqhkzKfG9oT+09do3uKZYa2rSOdMDr8RT6dGiVeqX4qgCYRWXbki5rmByvEELw8oqzLXNdgCx9Ygt5e0Ley1EcbIYCz2JQdkwgi3XeLS8mWy5+lsOr1e0uf/fckZVwC7B112KgFbS99LMpPhU76p9i4ORV1i8sp+7KRxTps9P+7uWmYPEeMef3epW9HkhnRyqjFM5L00mcU/SismfaPrSMeRZgb2Chr7bzn6xlJ3jRMniPGvH5v6UsEydcCJb8VeBnZ4bz0kWxPg4zOOzNNPg0l9i0lI3Xv+vONwuSZYszr95a+RJA0QD6K7Dte+ki2lezcLRAe1MxqvG8yVEyeMHi8fh/SZw+SYVoDyOyrlllze+lnmdXKaoG+BWyTzoJev3biqmJywjCnU+z1e48+e5AMdmTH0hqOMa2XPoZnpakW4EHNz95N7frPWahics46+67z+r1HXypI/i4bsi7JPD8meeljeFaaagGWfNZ+YVQxebr48fq9R18kSIbpCl9UPI2xs5c+hmelOW8L6AH9BAsIW/byussgFZMuc+2G2Ov3Mfrs70l2rSUB+Edb9wU4XqlYTF76RYaV4GwtELD049ogaYarmDRLnMbR6/cx+iIjyY45GU0+71wvnXrpl/jV+jO0gIDPKJLPMFeNIgcmq5gcGGSvl16/T9EXHUliTAnCZ2j8a4io74a99Ht1WJXrOBYQfu6qZTD3pTC3ZsPmQPCKyQOT7K7A6/c5+tIjSYx5X/mxhOp9xztjZS/9DKtadU4WEMb4gIF3IvnB5SQBMtivYnLHQPL6fYm++EgS20oonu6Alx98XQSvl542aqoWEG7AGL9fmWKa3TNoxWTPHLu68Pp9if4oQRKLBpDxe4axmzgE1mj6XXmtClPcAsIXo8ivhC/Xi+MeQb0Y9vCutOss4PV7DP3/zwxaSzXTwioAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$\\displaystyle \\operatorname{tr}\\left(\\left(- T^{T} + \\tilde W^{T} \\tilde X^{T}\\right) \\left(- T + \\tilde X \\tilde W\\right) \\right)$"
      ],
      "text/plain": [
       "  ⎛⎛  T           T         T⎞                         ⎞\n",
       "tr⎝⎝-T  + \\tilde W ⋅\\tilde X ⎠⋅(-T + \\tilde X⋅\\tilde W)⎠"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Trace(Err)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each of the elements inside the representation of the trace takes the form\n",
    "\n",
    "$$\n",
    "    (\\tilde w^T_k\\tilde x^{(n)} - T^{(n)}_k)^2\n",
    "$$\n",
    "\n",
    "Where\n",
    "* $\\tilde w^T_k\\tilde x^{(n)}$ is the model prediction for the $n$-th observation considering the $k$-th model\n",
    "* $T^{(n)}_k$ is whether the $n$-th observation is of class $k$.\n",
    "\n",
    "Thus, we would like to find $\\tilde{\\bf W}$ such that, $\\forall \\ k, n$,\n",
    "$$\n",
    "    \\tilde w^T_k\\tilde x^{(n)} \\approx 1 \\iff T^{(n)}_k = 1\n",
    "$$\n",
    "\n",
    "$$\n",
    "    \\tilde w^T_k\\tilde x^{(n)} \\approx 0 \\iff T^{(n)}_k = 0\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left(- T_{0, 0} + \\tilde W_{0, 0} \\tilde X_{0, 0} + \\tilde W_{1, 0} \\tilde X_{0, 1} + \\tilde W_{2, 0} \\tilde X_{0, 2} + \\tilde W_{3, 0} \\tilde X_{0, 3}\\right)^{2} + \\left(- T_{1, 0} + \\tilde W_{0, 0} \\tilde X_{1, 0} + \\tilde W_{1, 0} \\tilde X_{1, 1} + \\tilde W_{2, 0} \\tilde X_{1, 2} + \\tilde W_{3, 0} \\tilde X_{1, 3}\\right)^{2} + \\left(- T_{2, 0} + \\tilde W_{0, 0} \\tilde X_{2, 0} + \\tilde W_{1, 0} \\tilde X_{2, 1} + \\tilde W_{2, 0} \\tilde X_{2, 2} + \\tilde W_{3, 0} \\tilde X_{2, 3}\\right)^{2} + \\left(- T_{3, 0} + \\tilde W_{0, 0} \\tilde X_{3, 0} + \\tilde W_{1, 0} \\tilde X_{3, 1} + \\tilde W_{2, 0} \\tilde X_{3, 2} + \\tilde W_{3, 0} \\tilde X_{3, 3}\\right)^{2} + \\left(- T_{4, 0} + \\tilde W_{0, 0} \\tilde X_{4, 0} + \\tilde W_{1, 0} \\tilde X_{4, 1} + \\tilde W_{2, 0} \\tilde X_{4, 2} + \\tilde W_{3, 0} \\tilde X_{4, 3}\\right)^{2}$"
      ],
      "text/plain": [
       "                                                                              \n",
       "(-T₀₀ + \\tilde W₀₀⋅\\tilde X₀₀ + \\tilde W₁₀⋅\\tilde X₀₁ + \\tilde W₂₀⋅\\tilde X₀₂ \n",
       "\n",
       "                        2                                                     \n",
       "+ \\tilde W₃₀⋅\\tilde X₀₃)  + (-T₁₀ + \\tilde W₀₀⋅\\tilde X₁₀ + \\tilde W₁₀⋅\\tilde \n",
       "\n",
       "                                                    2                         \n",
       "X₁₁ + \\tilde W₂₀⋅\\tilde X₁₂ + \\tilde W₃₀⋅\\tilde X₁₃)  + (-T₂₀ + \\tilde W₀₀⋅\\ti\n",
       "\n",
       "                                                                              \n",
       "lde X₂₀ + \\tilde W₁₀⋅\\tilde X₂₁ + \\tilde W₂₀⋅\\tilde X₂₂ + \\tilde W₃₀⋅\\tilde X₂\n",
       "\n",
       "  2                                                                           \n",
       "₃)  + (-T₃₀ + \\tilde W₀₀⋅\\tilde X₃₀ + \\tilde W₁₀⋅\\tilde X₃₁ + \\tilde W₂₀⋅\\tild\n",
       "\n",
       "                              2                                               \n",
       "e X₃₂ + \\tilde W₃₀⋅\\tilde X₃₃)  + (-T₄₀ + \\tilde W₀₀⋅\\tilde X₄₀ + \\tilde W₁₀⋅\\\n",
       "\n",
       "                                                          2\n",
       "tilde X₄₁ + \\tilde W₂₀⋅\\tilde X₄₂ + \\tilde W₃₀⋅\\tilde X₄₃) "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Err[0,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left(- T_{0, 1} + \\tilde W_{0, 1} \\tilde X_{0, 0} + \\tilde W_{1, 1} \\tilde X_{0, 1} + \\tilde W_{2, 1} \\tilde X_{0, 2} + \\tilde W_{3, 1} \\tilde X_{0, 3}\\right)^{2} + \\left(- T_{1, 1} + \\tilde W_{0, 1} \\tilde X_{1, 0} + \\tilde W_{1, 1} \\tilde X_{1, 1} + \\tilde W_{2, 1} \\tilde X_{1, 2} + \\tilde W_{3, 1} \\tilde X_{1, 3}\\right)^{2} + \\left(- T_{2, 1} + \\tilde W_{0, 1} \\tilde X_{2, 0} + \\tilde W_{1, 1} \\tilde X_{2, 1} + \\tilde W_{2, 1} \\tilde X_{2, 2} + \\tilde W_{3, 1} \\tilde X_{2, 3}\\right)^{2} + \\left(- T_{3, 1} + \\tilde W_{0, 1} \\tilde X_{3, 0} + \\tilde W_{1, 1} \\tilde X_{3, 1} + \\tilde W_{2, 1} \\tilde X_{3, 2} + \\tilde W_{3, 1} \\tilde X_{3, 3}\\right)^{2} + \\left(- T_{4, 1} + \\tilde W_{0, 1} \\tilde X_{4, 0} + \\tilde W_{1, 1} \\tilde X_{4, 1} + \\tilde W_{2, 1} \\tilde X_{4, 2} + \\tilde W_{3, 1} \\tilde X_{4, 3}\\right)^{2}$"
      ],
      "text/plain": [
       "                                                                              \n",
       "(-T₀₁ + \\tilde W₀₁⋅\\tilde X₀₀ + \\tilde W₁₁⋅\\tilde X₀₁ + \\tilde W₂₁⋅\\tilde X₀₂ \n",
       "\n",
       "                        2                                                     \n",
       "+ \\tilde W₃₁⋅\\tilde X₀₃)  + (-T₁₁ + \\tilde W₀₁⋅\\tilde X₁₀ + \\tilde W₁₁⋅\\tilde \n",
       "\n",
       "                                                    2                         \n",
       "X₁₁ + \\tilde W₂₁⋅\\tilde X₁₂ + \\tilde W₃₁⋅\\tilde X₁₃)  + (-T₂₁ + \\tilde W₀₁⋅\\ti\n",
       "\n",
       "                                                                              \n",
       "lde X₂₀ + \\tilde W₁₁⋅\\tilde X₂₁ + \\tilde W₂₁⋅\\tilde X₂₂ + \\tilde W₃₁⋅\\tilde X₂\n",
       "\n",
       "  2                                                                           \n",
       "₃)  + (-T₃₁ + \\tilde W₀₁⋅\\tilde X₃₀ + \\tilde W₁₁⋅\\tilde X₃₁ + \\tilde W₂₁⋅\\tild\n",
       "\n",
       "                              2                                               \n",
       "e X₃₂ + \\tilde W₃₁⋅\\tilde X₃₃)  + (-T₄₁ + \\tilde W₀₁⋅\\tilde X₄₀ + \\tilde W₁₁⋅\\\n",
       "\n",
       "                                                          2\n",
       "tilde X₄₁ + \\tilde W₂₁⋅\\tilde X₄₂ + \\tilde W₃₁⋅\\tilde X₄₃) "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Err[1, 1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left( 2, \\  2\\right)$"
      ],
      "text/plain": [
       "(2, 2)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Err.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Understanding the Derivative\n",
    "$$\n",
    "    \\frac{\\partial}{\\partial \\tilde{\\bf W}}\\text{Tr}\\left\\{\\left(\\tilde{\\bf X}\\tilde{\\bf W} - T\\right)^T \\left(\\tilde{\\bf X}\\tilde{\\bf W} - T\\right)\\right\\} = 2\\tilde{\\bf X}^T\\left(\\tilde{\\bf X} \\tilde{\\bf W} - T\\right)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}B_{0, 0} C_{0, 0} + B_{0, 1} C_{1, 0} & B_{0, 0} C_{0, 1} + B_{0, 1} C_{1, 1}\\\\B_{1, 0} C_{0, 0} + B_{1, 1} C_{1, 0} & B_{1, 0} C_{0, 1} + B_{1, 1} C_{1, 1}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡B₀₀⋅C₀₀ + B₀₁⋅C₁₀  B₀₀⋅C₀₁ + B₀₁⋅C₁₁⎤\n",
       "⎢                                    ⎥\n",
       "⎣B₁₀⋅C₀₀ + B₁₁⋅C₁₀  B₁₀⋅C₀₁ + B₁₁⋅C₁₁⎦"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B = MatrixSymbol(\"B\", 2, 2)\n",
    "C = MatrixSymbol(\"C\", 2, 2)\n",
    "\n",
    "A = (B @ C).as_explicit()\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "trAA = A.T @ A\n",
    "trAA = trAA[0, 0] + trAA[1, 1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left(B_{0, 0} C_{0, 0} + B_{0, 1} C_{1, 0}\\right)^{2} + \\left(B_{0, 0} C_{0, 1} + B_{0, 1} C_{1, 1}\\right)^{2} + \\left(B_{1, 0} C_{0, 0} + B_{1, 1} C_{1, 0}\\right)^{2} + \\left(B_{1, 0} C_{0, 1} + B_{1, 1} C_{1, 1}\\right)^{2}$"
      ],
      "text/plain": [
       "                   2                      2                      2            \n",
       "(B₀₀⋅C₀₀ + B₀₁⋅C₁₀)  + (B₀₀⋅C₀₁ + B₀₁⋅C₁₁)  + (B₁₀⋅C₀₀ + B₁₁⋅C₁₀)  + (B₁₀⋅C₀₁ \n",
       "\n",
       "          2\n",
       "+ B₁₁⋅C₁₁) "
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trAA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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x7tH/Hm3aC4tefe3Vrr1w0HJ79b3ELvDyxvdzy6UhHdMlTydQONkIXhoPyvRoU8tQ9Oh/jzbthUmvvvZq1144aLm9+l7LrsMnAgT7Lp4G5K0FHfsj8z3a1DIePfrfo017YdKrr73atRcOWm6vvlexS5aGnsNjPRh/xeAsr2PqYIz8iMCIwIjAiMAVjQCeIPhiDvcJJTH/XiYC/dYOCd5iIngtlOM8IjAiMCIwInD1I4CJgC8C6H8jQKe+/wtUF5N0WRqT7gAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}B_{0, 0} C_{0, 0} + B_{0, 1} C_{1, 0} & B_{0, 0} C_{0, 1} + B_{0, 1} C_{1, 1}\\\\B_{1, 0} C_{0, 0} + B_{1, 1} C_{1, 0} & B_{1, 0} C_{0, 1} + B_{1, 1} C_{1, 1}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡B₀₀⋅C₀₀ + B₀₁⋅C₁₀  B₀₀⋅C₀₁ + B₀₁⋅C₁₁⎤\n",
       "⎢                                    ⎥\n",
       "⎣B₁₀⋅C₀₀ + B₁₁⋅C₁₀  B₁₀⋅C₀₁ + B₁₁⋅C₁₁⎦"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(B @ C).as_explicit()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
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    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
